We present a proof of convergence of the Hamiltonian Monte Carlo algorithm in terms of Functional Analysis. We represent the algorithm as an operator on the density functions, and prove the convergence of iterations of this operator in $L^p$, for $1<p<\infty$, and strong convergence for $2\le p<\infty$.
翻译:我们提出了汉密尔顿蒙特卡洛算法在功能分析方面的趋同证据。 我们代表算法作为密度函数的操作员,并证明该操作员的迭代以1美元兑1美元兑1美元和2美元兑2美元兑1美元兑1美元相趋同。